Subgroups — C₆₇×Dic₁₃⋊C₉ #44535582

Order 31356.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₇×C₁₃⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₁₃×C₆₇	C₃	1	1	yes	maximal, characteristic
3	C₆₇×C₁₃⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₃×C₆₇	C₂×C₃	1	1	yes	characteristic
5	Dic₁₃×C₆₇	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₃×C₆₇	C₃×C₄	1	1	yes	characteristic
7	C₄×C₉×C₆₇	—	13	1	no	maximal, Hall
8	C₂×C₁₃×C₆₇	C₂×C₉	1	1	yes	characteristic
9	C₂×C₉×C₆₇	—	13	1	no	—
10	C₁₃×C₆₇	C₄×C₉	1	1	yes	characteristic, complemented, Hall
11	C₃×C₄×C₆₇	—	13	1	no	—
12	C₉×C₆₇	—	13	1	no	Hall
13	Dic₁₃⋊C₉	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₃×C₆₇	D₁₃⋊C₃	1	1	yes	characteristic
15	C₄×C₆₇	—	13	1	no	Hall
16	C₂×C₁₃⋊C₉	C₂×C₆₇	1	1	yes	characteristic
17	C₃×C₆₇	Dic₁₃⋊C₃	1	1	yes	characteristic
18	C₃×Dic₁₃	C₃×C₆₇	1	1	yes	characteristic
19	C₂×C₆₇	D₁₃⋊C₉	1	1	yes	characteristic
20	C₁₃⋊C₉	C₄×C₆₇	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₁₃	C₂×C₃×C₆₇	1	1	yes	characteristic
22	C₆₇	Dic₁₃⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
23	Dic₁₃	C₉×C₆₇	1	1	yes	characteristic, complemented, Hall
24	C₃×C₁₃	C₃×C₄×C₆₇	1	1	yes	characteristic
25	C₄×C₉	—	13	1	no	Hall
26	C₂×C₁₃	C₂×C₉×C₆₇	1	1	yes	characteristic
27	C₂×C₉	—	13	1	no	—
28	C₁₃	C₄×C₉×C₆₇	1	1	yes	characteristic, complemented, Sylow
29	C₃×C₄	—	13	1	no	—
30	C₉	—	13	1	no	Sylow
31	C₂×C₃	C₆₇×D₁₃⋊C₃	1	1	yes	characteristic
32	C₄	—	13	1	no	Sylow
33	C₃	C₆₇×Dic₁₃⋊C₃	1	1	yes	characteristic
34	C₂	C₆₇×D₁₃⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₆₇	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₄×C₉×C₆₇
Frattini	C₂×C₃	C₆₇×D₁₃⋊C₃
Fitting, socle, prime radical	C₂×C₃×C₁₃×C₆₇	C₂×C₃
cosocle	C₂×C₃×C₁₃	C₂×C₃×C₆₇
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₆₇

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₆₇×C₁₃⋊C₉	C₄	semidirect
5. Dic₁₃×C₆₇	C₉	semidirect
10. C₁₃×C₆₇	C₄×C₉	semidirect
13. Dic₁₃⋊C₉	C₆₇	direct (N × H)
20. C₁₃⋊C₉	C₄×C₆₇	semidirect
22. C₆₇	Dic₁₃⋊C₉	direct (N × H)
23. Dic₁₃	C₉×C₆₇	semidirect
28. C₁₃	C₄×C₉×C₆₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₆₇×C₁₃⋊C₉	2
C₃×Dic₁₃×C₆₇	3
C₄×C₉×C₆₇	13
Dic₁₃⋊C₉	67

Subgroups — C67×Dic13⋊C9 #44535582

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×Dic₁₃⋊C₉ #44535582